REGRESSION AND CORRELATION EDDIE SEVA SEE
Summary
TLDRThis educational video script delves into the concepts of regression and correlation using Excel. It explains regression as a statistical method for estimating dependent variable values based on independent variables, utilizing the least squares method to determine the regression line's slope and y-intercept. The script provides a step-by-step guide on implementing simple linear regression in Excel, including calculating predicted values. It also explores correlation, specifically Pearson's R, to measure the strength and direction of the relationship between two variables. The script concludes with a discussion on the implications of these statistical measures for research and decision-making.
Takeaways
- ๐ **Regression Analysis**: Regression is a statistical method used to estimate the value of a dependent variable based on the value of an independent variable, minimizing the sum of squared differences.
- ๐ **Minimizing Errors**: The regression line is determined by minimizing the squared sum of the differences between the actual and estimated values of the dependent variable.
- โ๏ธ **Partial Derivatives**: Partial derivatives are applied to find the slope (B) and y-intercept (a) of the regression line, which are crucial for the linear regression equation.
- ๐ **Slope and Y-Intercept**: The slope indicates how much the dependent variable changes with each unit change in the independent variable, while the y-intercept is the value of the dependent variable when the independent variable is zero.
- ๐ **Excel Implementation**: Excel can be used to perform linear regression by programming formulas for B, A, and Y_current, allowing for predictions based on historical data.
- ๐ฎ **Forward and Backward Estimation**: Regression allows for both forward estimation (predicting future values) and backward estimation (estimating past values) based on the regression formula.
- ๐ **Correlation**: Correlation measures the statistical relationship between an independent and a dependent variable, with Pearson R being a common measure to determine the strength and direction of this relationship.
- ๐ **Negative Correlation**: A negative correlation indicates that as the independent variable increases, the dependent variable decreases, and vice versa.
- ๐ **Excel for Correlation**: Excel can calculate Pearson R quickly using its statistical functions, providing insights into the relationship between two variables.
- ๐ **Inferential Statistics**: In research, inferential statistics is important for generalizing findings from a sample to a larger population, often involving significance tests to validate relationships.
Q & A
What is the definition of regression as discussed in the script?
-Regression is a statistical process of estimating the value of the dependent variable, given the value of the independent variable, using the regression line determined by minimizing the square of the sum of the differences between the true or historical value of the dependent variable and the estimated value.
How does the slope of the regression line (B) provide information about the dependent variable?
-The slope of the regression line (B) indicates how much the value of the dependent variable changes for every unit change of the value of the explanatory variable.
What is the significance of the y-intercept (a) in a regression model?
-The y-intercept (a) gives the value of the dependent variable when the value of the explanatory variable is zero.
What method is used to determine the formulas for the slope (B) and y-intercept (a) in a regression model?
-The formulas for the slope (B) and y-intercept (a) are determined by applying partial derivatives to the equation of the sum squared errors and solving for the minimum.
How can Excel be used to perform linear regression?
-Excel can be used to perform linear regression by programming the formulas for B, A, and Y current in the respective cells and using the historical data to solve for the values of A and B.
What is the simple linear regression formula used in Excel as mentioned in the script?
-The simple linear regression formula used in Excel is Y current equals a plus B times X.
Can you explain the concept of correlation as discussed in the script?
-Correlation is a statistical relationship between an independent or explanatory variable and a dependent variable. It measures the extent to which the same individual occupies the same relative position on two variables.
What is the role of Pearson R in determining the correlation between two variables?
-Pearson R is used to determine the measure of correlation between two variables. It represents how closely the trend between two sets of data from the explanatory and dependent variables aligns.
How can Excel be used to compute the Pearson correlation coefficient?
-Excel can compute the Pearson correlation coefficient by using the 'Pearson' function under the statistical category in the formulas menu, where you input the ranges for the two variables.
What does a negative Pearson correlation coefficient indicate about the relationship between two variables?
-A negative Pearson correlation coefficient indicates that as the value of the independent variable increases, the value of the dependent variable decreases, and vice versa.
How can the magnitude of the Pearson correlation coefficient be interpreted in terms of the relationship between variables?
-The magnitude of the Pearson correlation coefficient indicates the strength and direction of the linear relationship between two variables. A coefficient close to -1 or 1 indicates a strong relationship, while a coefficient close to 0 indicates a weak relationship.
Outlines
๐ Introduction to Regression and Correlation in Excel
This paragraph introduces the concepts of regression and correlation using Excel. Regression is explained as a statistical method for estimating the value of a dependent variable based on the value of an independent variable, using the regression line. The process involves minimizing the sum of squared differences between the actual and estimated values of the dependent variable. The paragraph details how to calculate the slope (B) and y-intercept (a) of the regression line using partial derivatives. It also provides a practical example of predicting sugar sales for week 12 based on historical data from weeks one to ten. The process of inputting formulas in Excel to calculate the regression coefficients and predict future values is described, culminating in an example where the predicted sales for week 12 are shown as 30.2242 units.
๐ Exploring Correlation and its Significance
The second paragraph delves into the concept of correlation, specifically using Pearson's R to measure the statistical relationship between an independent and a dependent variable. It emphasizes that while correlation can indicate the strength and direction of a relationship, it does not prove causation. An example is provided where the relationship between the price and demand for sugar over ten weeks is analyzed. The paragraph explains how to use Excel's statistical functions to compute Pearson's R, and it discusses the interpretation of a negative correlation coefficient, indicating an inverse relationship between the price of sugar and its demand. The significance of this relationship is highlighted, showing how a strong negative correlation suggests that an increase in price leads to a decrease in demand, and vice versa.
๐ The Implications of Correlation in Research
The final paragraph discusses the implications of correlation measurements in research, particularly the difference between findings from probability and non-probability samples. It points out that while non-probability samples limit conclusions to the sample itself, probability samples allow for broader inferences about the population. The paragraph underscores the importance of inferential statistics in research, suggesting that correlation measures can indicate trends that are likely to be true in the broader population. It concludes by summarizing the discussion on regression and correlation, thanking the audience for their engagement.
Mindmap
Keywords
๐กRegression
๐กCorrelation
๐กDependent Variable
๐กIndependent Variable
๐กLinear Regression
๐กSlope
๐กY-Intercept
๐กPartial Derivatives
๐กPearson R
๐กExcel
Highlights
Regression is a statistical process for estimating the value of a dependent variable based on the value of an independent variable.
The regression line is determined by minimizing the sum of the squared differences between the actual and estimated values.
Partial derivatives are used to find the slope and y-intercept of the regression line.
The slope of the line indicates the change in the dependent variable for each unit change in the explanatory variable.
The y-intercept represents the value of the dependent variable when the explanatory variable is zero.
The simple linear regression formula is Y_current = a + BX, where a and B are constants derived from the data.
Historical data is necessary to solve for the values of a and B in the regression formula.
Excel can be used to program and solve for the values of a and B in a regression model.
An example is provided to illustrate how to estimate future sales of sugar using regression.
Correlation measures the statistical relationship between an independent and a dependent variable.
Pearson R is a measure of correlation that indicates the extent to which two variables move in relation to each other.
A negative correlation suggests that as one variable increases, the other decreases, and vice versa.
Excel can be used to compute the Pearson R value for a set of data to determine the strength and direction of the correlation.
A strong negative correlation between price and demand for sugar suggests that higher prices lead to lower demand.
Correlation measures do not prove causation, but they can indicate a relationship between variables.
The significance of the correlation can be tested to determine if the trend is likely to hold in the population.
Inferential statistics is crucial for extending findings from a sample to a broader population.
The lecture concludes with a summary of the discussed topics: regression and correlation.
Transcripts
hello students and fellow researchers
I am going to discuss
regression and correlation using Excel
regression is a statistical process of
estimating the value of the dependent
variable forward or backward
given the value of that independent
variable
using the regression line
determined by minimizing the square of
the sum of the difference between the
true or historical value of the
dependent variable
and estimated value of the same
using partial derivatives
and determining the formulas or
solutions for the slope of the line and
the y-intercept
the slope of the line provides
information on how much the value of the
dependent variable changes
for every unit change of the value of
the explanatory variable
the y-intercept gives the value of the
dependent variable when the value of the
explanatory variable is zero
applying partial derivatives with
respect to a and with respect to B to
the equation of the sum
squared errors results to the following
equations which are actually the
equations for a and b
the values of A and B using the
corresponding formulas can be
substituted to the equation Y current
equals a plus BS
as shown
the minimization process yields the
formula for the slope of the line B and
the y-intercept a
values which can be solved when the
historical data of the variables are
collected or observed
when b and a are determined they serve
as the constant a and the coefficient B
of the simple linear regression formula
why current equals a plus BX
let us now consider as an illustration
for the simple linear regression this
case
for the consecutive's weeks one to ten
the sales in units for sugar each week
are shown in the data set shown in the
next template
what would be the sales for sugar at
week 12.
this is
the
Excel sheet showing the collected or
historical data
for which
X and sales y
in other words
what is y current when X is 12.
to be able to use the linear regression
why Clarity equals a plus BX we must
solve for the values of A and B
we need to program in Excel the formulas
for B A and Y current
this is the Excel sheet that shows the
programming
encode the following programs in the
respective cells So the instructions are
given in the space
and of course the Excel sheet
is also shown where the programs are
inputted
in continuation this page also shows the
other
programs
another page for the continuation of the
programs
and actually
finally
in j6
the answer is given that is 30.2242
regression enabled us to estimate
forward the value of the dependent
variable at least 12.
in as much as the solution has been
programmed
or any new higher value of x the Excel
sheet will automatically predict the
value of y if you make use of any
earlier value of x a backward estimate
of the value i y will also be performed
by the formula
the forward or backward estimate of the
value of y is our process of regression
we proceed to the next topic correlation
correlation is a statistical
relationship between an independent or
explanatory variable and a dependent
variable
Pearson R is used
to
determine the measure of correlation
personal sample R represents the extent
to which the same individual
respondent object or subject
occupies the same relative position on
two variables
it shows how close the trend between two
sets of data from the explanatory and
dependent variables is
if the data are not from an experiment
the relationship will not prove
causation
this is our illustrative example
for the consecutive weeks one to ten the
demand and units and price per unit for
sugar each week
a shown in the data set in the next
template
what is the magnitude of relationship
between price of and demand for sugar
this is the formula for Pearson r
however we can use the program in Excel
for faster computation
this is the Excelsior showing the data
the price
versus the demand
for sure
to use the Excel program
click formulas
click more functions
click the statistical
click Pearson
the carry effects appears
type A2 colon a11 in array1
type B do colon b11 and array2
what does negative
0.98896 mean
the negative sign means that as the
value of the independent or explanatory
variable increases
the value of the dependent variable
decreases or
as the former decreases the latter
increases
the value negative
0.98896 further means
for every 100 percent increase in the
value of the independent variable
there is a
98.896 percent decrease in the value of
the dependent variable
or for every 100 percent decrease in the
value of the former
there is a
98.896 percent increase in the value of
the latter
this also means that
98.896 percent of the change in the
value of the dependent variable
can be accounted for or explained by the
100 change in the value of the team
dependent variable
measures of relationship or Association
present
the closeness of or the similarity in
the trend of the change in values of one
variable with respect to the change in
values of another variable
it shows the parallelism in the changes
in the two variables as in our previous
example between price of sugar and
demand for sugar
the very strong negative relationship
between the two could lead you to
hypothesize that as the price of sugar
grows higher
than in the demand for the product
lowers
if you computed a very very low
Association
for instance between number of trainings
and performance this could be a basis of
your premise
that the quantity of trainings would
have no bearing on your employees
performance
well the measure of Association
indicates the trend in the changes of
values
present in the samples of serving
they do not directly point to the trend
of values
in the entire population
in probability samples these measures of
relationship could actually show if the
trend is more likely true also in the
population represented
by testing the significance of the
relationship
in research undertakings
inferential statistics is very important
a non-probability example that does not
have a scientifically accepted support
for inferential analysis
commonly termed as significance tests
would have to limit the findings
conclusions and recommendations to the
research sample
from a probability sample however
the findings conclusions and
recommendations could be applied to the
concerned population of the study
today we have discussed regression and
correlation
thank you for listening reading
and viewing
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